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September 2015 p-adic Eisenstein–Kronecker series for CM elliptic curves and the Kronecker limit formulas
Kenichi Bannai, Hidekazu Furusho, Shinichi Kobayashi
Nagoya Math. J. 219: 269-302 (September 2015). DOI: 10.1215/00277630-2891995

Abstract

Consider an elliptic curve defined over an imaginary quadratic field K with good reduction at the primes above p5 and with complex multiplication by the full ring of integers OK of K. In this paper, we construct p-adic analogues of the Eisenstein–Kronecker series for such an elliptic curve as Coleman functions on the elliptic curve. We then prove p-adic analogues of the first and second Kronecker limit formulas by using the distribution relation of the Kronecker theta function.

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Kenichi Bannai. Hidekazu Furusho. Shinichi Kobayashi. "p-adic Eisenstein–Kronecker series for CM elliptic curves and the Kronecker limit formulas." Nagoya Math. J. 219 269 - 302, September 2015. https://doi.org/10.1215/00277630-2891995

Information

Received: 28 June 2012; Revised: 18 June 2014; Accepted: 14 August 2014; Published: September 2015
First available in Project Euclid: 20 October 2015

zbMATH: 1336.11050
MathSciNet: MR3413578
Digital Object Identifier: 10.1215/00277630-2891995

Subjects:
Primary: 11G55
Secondary: 11G07, 11G15, 14F30, 14G10

Rights: Copyright © 2015 Editorial Board, Nagoya Mathematical Journal

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Vol.219 • September 2015
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